Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.StringTokenizer;

public class CFR564B {
  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
//     InputStream inputStream = new FileInputStream("in.txt");
//     OutputStream outputStream = new FileOutputStream("out.txt");

    InputReader in = new InputReader(inputStream);
    PrintWriter out = new PrintWriter(outputStream);

//    Code here!
    int n = in.nextInt();
    int[] ansI, ansJ;
    ansI = new int[n];
    ansJ = new int[n];
    int sz = (n - 1) / 2;
    sz++;
    if (n % 2 == 0)
      sz++;

    int first = 1, last = n;
    int topI, topJ, bI, bJ;
    topI = topJ = 1;
    bI = bJ = sz;

    while (first < last) {
      ansI[first - 1] = topI;
      ansJ[first - 1] = topJ;

      ansI[last - 1] = bI;
      ansJ[last - 1] = bJ;

      topI++;
      if (topI == sz + 1) {
        topI = 1;
        topJ++;
      }

      bI--;
      if (bI == 0) {
        bI = sz;
        bJ--;
      }

      first++;
      last--;
    }
    if (first == last) {
      ansI[first - 1] = topI;
      ansJ[first - 1] = topJ;
    }

    out.println(sz);
    for (int i = 0; i < n; i++) {
//      out.println(i + 1 + ": " + ansI[i] + " " + ansJ[i]);
      out.println(ansI[i] + " " + ansJ[i]);
    }

    out.close();
  }

  static class InputReader{BufferedReader reader;StringTokenizer tokenizer;InputReader(InputStream stream){reader=new BufferedReader(new InputStreamReader(stream),32768);tokenizer=null;}String next(){while(tokenizer==null||!tokenizer.hasMoreTokens()){try{tokenizer=new StringTokenizer(reader.readLine());}catch(IOException e){throw new RuntimeException(e);}}return tokenizer.nextToken();}String nextLine(){try{return reader.readLine();}catch(IOException e){e.printStackTrace();}return"";}int nextInt(){return Integer.parseInt(next());}long nextLong(){return Long.parseLong(next());}}
}